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Furstenberg sumset conjecture and Mandelbrot percolations

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arxiv 2211.16410 v3 pith:OCWQXPLK submitted 2022-11-29 math.DS math.MGmath.PR

Catherine Bruce , Xiong Jin This is my paper · ORCID
classification math.DSmath.MGmath.PR
keywords mandelbrotmeasuresconvolutionsextendfurstenbergpercolationssumsettheorem
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In this paper we extend Hochman and Shmerkin's projection theorem to product measures of Mandelbrot cascades acting on ergodic measures imaged through canonical mappings of one-dimensional iterated function systems without any separation conditions. Consequently we extend Furstenberg sumset theorem to images of subshifts on symbolic spaces, and to Mandelbrot percolations on invariant sets. We also obtain dimension results for convolutions of Bernoulli convolutions and that of Mandelbrot cascade measures.

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  1. Smooth projections of self-similar measures

    math.DS 2026-07 accept novelty 8.0 of 10

    A spectral-gap criterion gives Sobolev regularity for prescribed projections of self-similar measures and yields explicit examples such as singular measures with all line projections smooth.

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